In this verbal reasoning odd one out question, you must identify which city name among Washington, New York, Las Vegas and Sydney does not belong to the same country as the others.

Introduction / Context:
This is a general knowledge and verbal reasoning odd one out question involving well known city names. Such questions often test a candidate awareness of world geography and the ability to group items according to a common attribute, such as country, continent, or political status. Here, three cities are from the same country, while one city is from a different country and continent.

Given Data / Assumptions:

• The options are Washington, New York, Las Vegas and Sydney.
• We interpret Washington as a major city in the United States, not as the broader state name.
• We assume standard geographical knowledge of countries and continents.

Concept / Approach:
The core concept is categorization by country. We check which cities belong to the same nation. Washington, New York and Las Vegas are all famous cities in the United States of America. Sydney, on the other hand, is a major city in Australia. Therefore, the odd one out is the city that does not belong to the United States. This type of question reinforces basic world geography and city country mapping which is useful for many competitive examinations.

Step-by-Step Solution:
Step 1: Washington is the capital city of the United States of America.Step 2: New York is a major city in the United States, located in the state of New York.Step 3: Las Vegas is also a city in the United States, located in the state of Nevada.Step 4: Sydney is a major coastal city in Australia and is not part of the United States; it is located in the state of New South Wales.Step 5: Since three cities are in the United States and one city is in Australia, the city that does not belong to the United States is the odd one out.
Verification / Alternative check:
You can verify the classification by recalling common country city pairs: Washington USA, New York USA, Las Vegas USA, Sydney Australia. This quick mental mapping confirms that Sydney stands apart by country and continent. Therefore, the geographical criterion unambiguously identifies Sydney as the odd city out.

Why Other Options Are Wrong:
Washington is not the odd one out because it belongs to the United States, just like New York and Las Vegas.
New York is again a United States city and shares the same national identity as Washington and Las Vegas.
Las Vegas is in the United States as well and therefore belongs to the same group as Washington and New York.

Common Pitfalls:
Some learners might overthink the question and consider population size, coastal location, or capital city status. While Washington is a capital and New York is a large financial hub, these differences do not isolate a single city in a consistent way. The cleaner and more reliable classification is by country. Failing to use the country based grouping may lead to confusion or subjective interpretations. Always look for an objective property that clearly separates one option from the rest.

Final Answer:
Only Sydney is a city in Australia, whereas Washington, New York and Las Vegas are cities in the United States of America, so Sydney is the odd one out.